Finite Group Databasebeta

← #13119827

Subgroups — #13119827

Order 1664.

604 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88142C211yesmaximal, characteristic, complemented
2C2×#88139C212yesmaximal
3C2×#88135C211yesmaximal, characteristic
4C13×#397C211yesmaximal, characteristic, complemented
5#11718654C211yesmaximal, characteristic, complemented
6#11718614C211yesmaximal, characteristic, complemented
7#11718603C212yesmaximal, complemented
8#11718335C211yesmaximal, characteristic, complemented
9#11718328C212yesmaximal, complemented
10#11718310C211yesmaximal, characteristic, complemented
11#11718307C212yesmaximal, complemented
12C22×C22⋊D13C2211yescharacteristic
13C23×Dic13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C22×Dic26C2212yes—
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2211yescharacteristic
18C2×C13×C22⋊C4C2212yes—
19C2×C22⋊Dic13C2212yes—
20C2×#6103C2211yescharacteristic
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×C4⋊Dic13C2211yescharacteristic
24C2×#6101C2211yescharacteristic
25C2×#6101C2212yes—
26C2×#6101C2212yes—
27C2×C4×Dic13C2212yes—
28C2×C4×Dic13C2211yescharacteristic
29#88142—24no—
30#88139—28no—
31#88135—24no—
32C13×#95C2212yes—
33C13×#95C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37#88071C2211yescharacteristic
38C24×C13C2311yescharacteristic
39C23×D13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×C4×C13C2312yes—
43C22×C4×C13C2311yescharacteristic
44C2×C22⋊D13—22no—
45C2×C22⋊D13—22no—
46C2×C22⋊D13D414yes—
47C22×Dic13—22no—
48C22×Dic13—24no—
49C22×Dic13C2311yescharacteristic
50C22×Dic13C2312yes—
51C22×Dic13C2312yes—
52C22×Dic13C2311yescharacteristic
53C22×Dic13C2311yescharacteristic
54C2×C4×D13—22no—
55C2×C4×D13—24no—
56C2×Dic26—24no—
57C2×Dic26—24no—
58C2×Dic26—24no—
59C13×C4⋊C4—22no—
60C13×C22⋊C4—24no—
61C13×C22⋊C4—22no—
62C22⋊Dic13—24no—
63#6103—24no—
64#6103—24no—
65#6103—22no—
66C4⋊Dic13—22no—
67#6101—22no—
68#6101—24no—
69#6101—24no—
70C4×Dic13—24no—
71C4×Dic13D414yes—
72#2547—131nomaximal, Sylow
73C23×C13—21no—
74C23×C13—22no—
75C23×C13—21no—
76C23×C13—22no—
77C23×C13C2×D412yes—
78C23×C13C2411yescharacteristic
79C22×D13—21no—
80C22×D13—22no—
81C22×D13—21no—
82C22×D13—22no—
83C22×D13C2×D412yes—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13C2×D412yes—
94C22⋊D13—28no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—21no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—44no—
104C2×Dic13C2×D412yes—
105C2×Dic13C2×D412yes—
106C2×Dic13C2×D412yes—
107C2×Dic13#4112yes—
108C2×Dic13#4114yes—
109C4×D13—44no—
110Dic26—48no—
111C2×C4⋊Q8—131no—
112C2×#124—132no—
113C2×C4×D4—131no—
114#397—131no—
115#397—131no—
116#397—131no—
117#397D1311yescharacteristic, complemented
118#391—132no—
119#380—132no—
120#380—132no—
121C4×C4⋊C4—131no—
122C22×C13—22no—
123C22×C13—24no—
124C22×C13—41no—
125C22×C13—41no—
126C22×C13—42no—
127C22×C13C22×D411yescharacteristic
128C22×C13C22×D411yescharacteristic
129C22×C13C2×#4111yescharacteristic
130C22×C13C2×#4112yes—
131C22×C132−1+412yes—
132C2×D13—22no—
133C2×D13—24no—
134C2×D13—41no—
135C2×D13—41no—
136C2×D13—42no—
137C4×C13—22no—
138C4×C13—42no—
139C4×C13—41no—
140C4×C13—42no—
141Dic13—42no—
142Dic13—41no—
143Dic13—42no—
144Dic13#12114yes—
145Dic13#12414yescomplemented
146C22×Q8—132no—
147C22×D4—131no—
148C23×C4—131no—
149C23×C4—131no—
150C4⋊Q8—264no—
151#124—268no—
152C4×D4—264no—
153C2×C4⋊C4—131no—
154C2×C4⋊C4—132no—
155C2×C4⋊C4—131no—
156C2×C4⋊C4—132no—
157C2×C4⋊C4C2×D1311yescharacteristic
158C2×C22⋊C4—132no—
159C2×C22⋊C4—131no—
160C2×C22⋊C4—132no—
161C2×C22⋊C4—132no—
162C2×C22⋊C4C2×D1311yescharacteristic
163C2×C22⋊C4C2×D1312yes—
164C2×C42—131no—
165C2×C42—132no—
166#95—131no—
167#95—132no—
168#95—132no—
169#95—132no—
170#95C2×D1311yescharacteristic
171#95C2×D1312yes—
172C2×C13—42no—
173C2×C13C2×#12111yescharacteristic
174C2×C13C2×#12411yescharacteristic
175C2×C13#53611yescharacteristic
176C2×C13#54712yes—
177C2×C13#55612yes—
178D13—42no—
179C24—131no—
180C24C22×D1311yescharacteristic
181C2×Q8—264no—
182C2×Q8—264no—
183C2×Q8—264no—
184C2×D4—134no—
185C2×D4—262no—
186C2×D4—262no—
187C22×C4—131no—
188C22×C4—131no—
189C22×C4—131no—
190C22×C4—132no—
191C22×C4—132no—
192C22×C4—262no—
193C22×C4—264no—
194C22×C4—262no—
195C22×C4—264no—
196C22×C4C22×D1311yescharacteristic
197C22×C4C22×D1312yes—
198C22×C4C22×D1312yes—
199C22×C4C22×D1311yescharacteristic
200C4⋊C4—22no—
201C4⋊C4—262no—
202C4⋊C4—264no—
203C4⋊C4—264no—
204C4⋊C4—262no—
205C22⋊C4—24no—
206C22⋊C4—22no—
207C22⋊C4—264no—
208C22⋊C4—264no—
209C22⋊C4—264no—
210C22⋊C4—262no—
211C42—134no—
212C42—264no—
213C13#254711yescharacteristic, complemented, Sylow
214C23—21no—
215C23—22no—
216C23—21no—
217C23—22no—
218C23—132no—
219C23—261no—
220C23—262no—
221C23—261no—
222C23—262no—
223C23D4×D1312yes—
224C23C23×D1311yescharacteristic
225Q8—528no—
226D4—268no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—132no—
237C2×C4—132no—
238C2×C4—132no—
239C2×C4—134no—
240C2×C4—132no—
241C2×C4—262no—
242C2×C4—262no—
243C2×C4—261no—
244C2×C4—262no—
245C2×C4—262no—
246C2×C4—262no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—524no—
250C2×C4—524no—
251C2×C4D4×D1312yes—
252C22—22no—
253C22—24no—
254C22—41no—
255C22—41no—
256C22—42no—
257C22—262no—
258C22—264no—
259C22—521no—
260C22—521no—
261C22—522no—
262C22C2×D4×D1311yescharacteristic
263C22C2×D4×D1311yescharacteristic
264C22#41×D1311yescharacteristic
265C22#41×D1312yes—
266C22#8825712yes—
267C4—22no—
268C4—42no—
269C4—42no—
270C4—41no—
271C4—134no—
272C4—134no—
273C4—522no—
274C4—522no—
275C4—521no—
276C2—42no—
277C2—522no—
278C2D13×#12111yescharacteristic
279C2#1171935311yescharacteristic
280C2#1171936012yes—
281C2D13×#12411yescharacteristic
282C2#1171940712yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#397C2
prime radicalC22×C22⋊D13C22
hypercenter#397D13
hypocenterC13#2547
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #397

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#88142C2semidirect
4. C13×#397C2semidirect
5. #11718654C2semidirect
6. #11718614C2semidirect
7. #11718603C2semidirect
8. #11718335C2semidirect
9. #11718328C2semidirect
10. #11718310C2semidirect
11. #11718307C2semidirect
117. #397D13semidirect
145. Dic13#124semidirect
213. C13#2547semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#881422
C2×#881392
C2×#881352
C13×#3972
#117186542
#117186142
#117186032
#117183352
#117183282
#117183102
#117183072
#254713